If (a, 1, 1), (1, b, 1) and (1, 1, c) are coplanar then prove that `(1)/(1-a)+(1)/(1-b)+(1)/(1-c)=1`.

If the lines ax + y + 1 = 0, x + by + 1 = 0 and x + y + c = 0 are concurrent then prove that, (1)/( 1-a) + (1) /( 1-b) + (1) /( 1-c) = .

If points (a,0), (0,b) and (1,1) are collinear , then (1)/(a) + (1)/(b) = . . . . .

If a^(2) + 2bc, b^(2) + 2ac, c^(2) + 2ab are in A.P then prove that (1)/(b-c), (1)/(c-a) and (1)/(a-b) are in A.P.

Show that the points (a, 0), (0, b) and (1, 1) are collinear, if (1)/(a)+(1)/(b)=1

Two systems of rectangular axis have the same origin. If a plane cuts them at distances a, b, c and a', b', c', respectively from the origin, then prove that (1)/(a^2)+(1)/(b^2)+(1)/(c^2)=(1)/((a')^2)+(1)/((b')^2)+(1)/((c')^2) .

Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then (1)/(a^2)+(1)/(b^2)+(1)/(c^2)=(1)/(p^2)

If A=[{:(2,3),(1,-4):}] and B=[{:(1,-2),(-1,3):}] then verify that (AB)^(-1)=B^(-1)A^(-1)

If A=[{:(2,3),(1,-4):}] and B=[{:(1,-2),(-1,3):}] then verify that (AB)^(-1)=B^(-1)A^(-1)

Show that the four points A(0,-1,0), B(2,1,-1), C(1,1,1) and D(3,3,0) are coplanar. Find the equation of the plane containing them.

If in a triangle ABC, /_C=60^@ , then prove that 1/(a+c)+1/(b+c)=3/(a+b+c)